Problem: In the right triangle shown, $AC = 5$ and $AB = 10$. What is $BC$ ? $A$ $C$ $B$ $5$ $?$ $10$
Answer: We know $a^2 + b^2 = c^2$ We want to find $a$ ; let $b = 5$ and $c = 10$ So $a^2 = c^2 - b^2 = 10^2 - 5^2 = 75$ Then, $a = \sqrt{75}$ Simplifying the radical gives $a = 5\sqrt{3}.$